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An  Analysis  of  Molecular  Volumes 

from  the  Point  of  View  of  the 

Lewis-Langmuir  Theory  of 

Molecular  Structure 


A  DISSERTATION 


PRESENTED  TO  THE 

FACULTY  OF  PRINCETON  UNIVERSITY 

IN  CANDIDACY  FOR  THE  DEGREE 

OF  DOCTOR  OF  PHILOSOPHY 


BY 


ROBERT  N.  PEASE 


-  &* 


Accepted  by  the  Department  of  Chemistry,  March,  1921. 


An  Analysis  of  Molecular  Volumes 

from  the  Point  of  View  of  the 

Lewis-Langmuir  Theory  of 

Molecular  Structure 


ROBERT  N.  PEASE 


AN  ANALYSIS  OF  MOLECULAR  VOLUMES  FROM  THE  POINT  OF 

VIEW  OF  THE  LEWIS-LANGMUIR  THEORY  OF 

MOLECULAR  STRUCTURE. 

According  to  the  Lewis^Langmuir2  theory  of  valence  and  atomic  and 
molecular  structure,  the  numbers  of  electrons  surrounding  the  positive 
nuclei  of  the  atoms  of  the  inert  gases  are  such  as  to  permit  of  particularly 
stable  arrangements.  The  atoms  of  the  other  elements  enter  into  com- 
bination in  such  a  manner  as  to  group  around  their  respective  nuclei,  by 
taking  up,  losing  or  sharing  electrons,  a  number  of  electrons  equal  to  that 
in  the  atoms  of  the  inert  gas  nearest  to  them  in  the  periodic  table.3  As  a 
result  of  this  tendency  the  number  of  electrons  about  the  positive  nuclei 
of  atoms  of  those  elements  which  tend  to  revert  to  the  same  rare  gas  is  the 
same,  when  the  atoms  are  in  combination.  Further,  it  sometimes  happens 
that  different  atoms  or  groups  of  atoms,  existing  alone  as  molecules  or 
acting  as  the  nuclear  atoms  of  compounds,  have  as  a  whole  the  same 
numbers  and  arrangements4  of  electrons  and  therefore  differ  only  in  the 
magnitude  and  distribution  of  the  charges  on  the  positive  nuclei  of  the 
atoms.  Such  compounds  and  groups  of  atoms  Langmuir5  calls  "iso- 
steres." Langmuir  has  pointed  out  the  marked  similarity  of  physical 
properties  of  pairs  of  isosteres  which  are  capable  of  independent  existence 
as  molecules,  such  as  nitrous  oxide  and  carbon  dioxide.  This  being  the 
case,  it  does  not  seem  improbable  that  the  volumes  of  isosteric  atoms  or 
groups  of  atoms,  whether  these  exist  as  free  molecules  or  as  the  nuclear 
atoms  of  a  compound,  may  be  the  same.  This  involves  the  assumption 
that  the  outer  shells  of  electrons  in  isosteres  have  the  same  dimensions 
independent  of  the  charges  on  the  positive  nuclei  of  the  atoms  or  at  least 
that  the  volume  of  the  molecule  as  a  whole  shall  behave  as  if  this  were 
the  case.6  The  remainder  of  this  paper  is  devoted  to  establishing  the 
fundamental  correctness  of  this  assumption  and  to  examining  the  evidence 

1  Lewis,  /.  Am.  Chem.  Soc.,  38,  762  (1916). 

2  Langmuir,  ibid.,  41,  868  (1919). 

1  It  is  not  to  the  particular  arrangements  of  electrons  in  the  inert  gases  that  the 
atoms  of  the  other  elements  tend  to  revert,  for  in  organic  compounds,  for  example,  the 
carbon  atoms  are  assumed  to  have  the  8  electrons  arranged  in  pairs  at  the  corners 
of  a  tetrahedron,  while  in  neon,  the  corresponding  rare  gas,  the  8  electrons  are  at  the 
corners  of  a  cube. 

4  This  is  always  to  be  understood  to  refer  to  all  the  electrons  in  the  molecule  or 
group  of  atoms,  not  merely  to  those  in  the  outer  shell. 

6  Langmuir,  J.  Am.  Chem.  Soc.,   41,  1543  (1919). 

6  See  note,  p.  1001. 


4535G5 


furnished  by  molecular  volumes  regarding  the  structure  of  certain  mole- 
cules and  nuclear  atoms. 

For  the  comparisons  of  molecular  volumes  the  values  of  the  quantity  6 
of  van  der  Waals'  equation  have  been  employed.  These  have  been 
calculated  from  the  relation  b  =  1/&RTc/pc  =  0.000458  Tc/pc  in  which, 
Tc  is  the  critical  temperature  in  degrees,  absolute;  and  pc  is  the  critical 
pressure  in  atmospheres.  The  values  of  the  critical  temperature  and 
pressure  and  of  b  are  given  in  Table  I.  The  results  of  Young  and  the 
recent  determinations  of  Cardoso  have  been  used  wherever  possible. 
TABLE  I.  —  THE  VALUES  OF  CRITICAL  TEMPERATURES  AND  PRESSURES,  AND  OF  VAN 

DER  WAALS'  b. 

Te  =  critical  temperature  in  degrees,  Kelvin. 

pc  =  critical  pressure  in  atmospheres. 

b  X  105  =  45.8  Tc/pc. 

Tc.  PC. 

Atmospheres. 

26.9 

48.0 

54.3 

58.2 

12.8 

45.6 
112.3 
217.5 

50.7 

49.3 

61.7 

33.7 

34.6 

64.6 

72.9 

71.7 

64.5 

89.1 

81.6 

48.9 

44.0 

33.0 

32.9 

29.6 

26.9 

24.6 

30.7 


°K. 

Ne 

44.7 

Ar 

150.7 

Kr 

210.5 

Xe 

289.7 

H2 

33.2 

CH4 

190.2 

NH3 

406.0 

H20 

647.0 

C2H4 

282.6 

02 

155.0 

C2H2 

308.6 

N2 

128.3 

CO 

134.4 

NO 

180.2 

C02 

304.0 

N20 

309.6 

PH8 

324.4 

H2S 

373.4 

HC1 

324.4 

C2H6 

305.2 

C3H8 

370 

n-C6H« 

470.3 

wo-C5Hi2 

460.9 

n-C6H14 

507.9 

«-C7Hi6 

539.9 

n-C8H18 

569.3 

(CH3)2CH.CH(CH8)2 

500.5 

(CH3)2CHCH2 

CH2CH(CH8)2 

549.9 

(CH,)20 

400.1 

(C2H6)20 

466.9 

C2H6NH2 

456.2 

(CH3)2NH 

437.6 

(C2H6)2NH 

496.3 

24.6 
53.0 
35.6 
55.5 
52.4 
36.6 


b  X  10». 

Observers.1 

76 

14 

144 

8 

177 

17 

228 

15 

119 

14 

191 

7 

165 

6 

136 

10 

225 

6 

144 

7 

229 

6 

174 

7 

178 

7 

128 

1 

191 

6 

198 

6 

230 

4 

192 

6 

182 

6 

286 

6 

386 

13 

652 

18 

641 

18 

785 

18 

919 

18 

1057 

18 

745 

18 

1025 
346 
600 
376 
382 
621 


18 
5 

18 
3 
3 
3 


1  Observers: 


TABLE  I  (continued}. 
Tc.  Pc. 

0  K.  Atmospheres  6  X  10».  Observers. 

[414.0  83.9  226  9 

Cli  |  419.0  93.5  205  11 

(417.0  76.1  252  16 

CC14  556.2  45.0  566  18 

GeCl4  550.0  38.0  663  12 

SnCl4  591.8  37.0  733  18 

C«H6  561.6  47.9  537  18 

C6H12  553.1  39.8  635  18 

C6H5CH3  593.7  41.6  653  2 

C6H5F  559.6  44.6  574  18 

C6H6C1  632.3  44.6  648  18 

C«H6Br  670.0  44.6  687°)  lg 

C6H5I  721.0  44.6  740a  J 

0  Calculated  by  Young. 

1.  Adwentowski,  Ion,  2,  1  (1910);  cf.  C.  A.,  4,  2777  (1910). 

2.  Altschuel,  Z.  physik.  Chem.,  11,  577  (1893). 

3.  Berthoud,  J.  chim.  phys.,  15,  3  (1917). 

4.  Briner,  ibid.,  4,  476  (1906). 

5.  Briner  and  Cardoso,  ibid.,  6,  641  (1908). 

6.  Cardoso,  J.  chim.  phys.,  10,  470  (1912). 

7.  Cardoso,  ibid.,  13,  312  (1915)). 

8.  Crommelin,  Comm.  Phys.  Lab.  Leiden,  115,  118  (1910). 

9.  Dewar,  Phil.  Mag.,  [5]  18,  210  (1884). 

10.  Holborn  and  Baumann,  Ann.  Phys.,  [4]  31,  945  (1910). 

11.  Knietsch,  Ann.,  259,  100  (1890). 

12.  Nilson  and  Pettersson,  Z.  physik.  Chem.,  1,  38  (1887). 

13.  Olszewski,  Phil.  Mag.,  [5]  39,  188  (1895). 

14.  Onnes,  Proc.  Acad.  Sci.  Amsterdam,  20,  178  (1917). 

15.  Patterson,  Cripps,  and  Whytlaw  Gray,  Proc.  Roy.  Soc.,  [A]  86,  579  (1912). 

16.  Pellaton,  J.  chim.  phys.,  13,  426  (1915). 

17.  Ramsay  and  Travers,  Phil.  Trans.  Roy.  Soc., '197,  47  (1901). 

18.  Young,  Sci.  Proc.  Roy.  Dublin  Soc.,  N.  S.  12,  374  (1909-10). 

Unfortunately,  lack  of  space  does  not  permit  an  extended  discussion 
of  the  recent  paper  of  J.  J.  Van  Laar1  on  the  additivity  of  the  quantity  b 
of  van  der  Waals'  equation.  He  has  assumed  arbitrary  and  sometimes 
variable  values  for  the  volumes  of  the  atoms  and  obtains  good  average 
agreement  between  calculated  and  observed  values.  His  atomic  volumes 
are,  however,  difficult  to  reconcile  with  the  Lewis-Langmuir  theory. 

The  paragraphs  immediately  following  deal  with  the  molecular  volumes 
of  those  compounds  which  contain  carbon,  nitrogen  and  oxygen  as  nuclear 
atoms. 

Methane,  Ammonia  and  Water. — The  nuclear  carbon,  nitrogen  and 
oxygen  atoms  in  methane,  ammonia  and  water,  respectively,  are  isosteric 
since  each  consists  of  a  positive  nucleus  and  pair  of  electrons  surrounded 

1  Van  Laar,  /.  chim.  phys.,  14,  3  (1916). 


by  an  octet  of  electrons.  If  these  isosteric  nuclear  atoms  have  the  same 
volume,  then  the  differences  in  volume  between  pairs  of  these  substances 
will  be  the  volume  of  the  extra  hydrogen  atoms  one  contains  over  the 
other.  The  volumes  of  the  compounds  are,  methane,  191;  ammonia, 
165;  water,  136.  Methane  has  one  more  hydrogen  than  ammonia  and  is 
greater  by  26  units.  Ammonia  has  one  more  hydrogen  than  water  and  is 
greater  by  29  units.  It  should  be  remembered  that  the  errors  in  the 
volumes  fall  on  these  differences.  Taking  the  average  difference  of  28 
as  the  volume  of  one  hydrogen  atom  in  these  compounds  and  subtracting 
foi  the  total  number  of  hydrogen  atoms  from  the  volume  of  each  com- 
pound, to  find  the  volumes  of  the  nuclear  atoms,  one  obtains  for  the  latter 
the  values 

CH4  :  191-112  =  79 

NH3  :  165-84     =  81    Average  80. 

H20  :  136-56     =  80 

The  nuclear  atoms  are  seen  to  have  almost  exactly  equal  volumes, 
substantiating  the  assumption  made. 

For  neon,  the  corresponding  inert  gas,  the  volume  is  76.  That  the 
volume  of  the  nuclear  atoms  in  the  above  compounds  is  practically  the 
same  (80)  would  seem  to  indicate  that  these  atoms  are  essentially  cubic, 
as  neon  is  assumed  to  be.  The  tendency  of  the  hydrogen  atoms  to  draw 
together  the  pairs  of  electrons,  by  means  of  which  they  are  held,  to  give 
the  nuclear  atom  a  tetrahedral  structure,  is  apparently  not  great.  That 
the  volume  of  the  nuclear  atoms  and  that  of  neon  are  not  more  nearly 
equal  may  be  due  to  slight  deformation  of  the  cubic  structures  in  the 
hydrides  or  to  the  inaccuracy  of  the  value  for  neon,  the  critical  data 
for  which  are  given  by  Kammerlingh  Onnes  as  preliminary. 

Ethylene  and  Oxygen.  —  Elementary  oxygen  and  the  carbon  atoms 
in  ethylene  are  isosteric.  In  both,  the  positive  nuclei  (with  a  pair  of 
electrons  each)  are  surrounded  by  12  electrons  forming  two  tetrahedral 
octets  sharing  two  pairs,  that  is,  meeting  along  an  edge.  If  the  volumes 
of  the  two  isosteres  are  the  same,  the  difference  in  volume  between 
ethylene  (255)  and  oxygen  (144)  represents  the  volume  of  the  4  hydrogen 
atoms  in  ethylene.  One-fourth  of  this  difference  should  be  the  volume 
of  one  hydrogen. 


4  4 

The  volume  of  one  hydrogen  is  found  to  be  28  as  in  methane  and  the 
like. 

Acetylene,  Nitrogen  and  Carbon  Monoxide.  —  For  reasons  to  be  dis- 
cussed later,  nitrogen  and  carbon  monoxide  are  assumed  to  have  the 
normal,  acetylenic,  rather  than  the  condensed  structure  suggested  by 
Langmuir.  Thus,  nitrogen,  carbon  monoxide,  and  the  carbon  atoms  of 


acetylene  are  isosteric,  since  the  structure  for  all  consists  of  two  posi- 
tive nuclei  (with  a  pair  of  electrons  each)  surrounded  by  two  tetrahedral 
octets  composed  of  10  electrons,  3  pairs  being  shared,  that  is,  meeting  face 
to  face. 

The  volumes  of  nitrogen  and  carbon  monoxide  are  174  and  178,  respec- 
tively, that  of  the  unsymmetrical  carbon  monoxide  being  slightly  the 
greater.  Taking  symmetrical  nitrogen  to  compare  with  the  symmetrical 
carbon  atoms  of  acetylene  (229),  it  is  found  that  one-half  the  difference 
between  the  volumes  of  the  two  compounds,  which  should  equal  the 
volume  of  one  hydrogen  atom,  is  again  28. 

VcsHs-^N,       229  —  174 
-2~  — 

It  is  convenient  to  point  out  here  that  the  volumes  of  cart  on  dioxide 
and  nitrous  oxide,  which  are  isosteric,  are  191  and  198,  respectively. 
If  nitrous  oxide  has  the  structure  N  =  N  =  O,  as  Langmuir  is  inclined 
to  think,  then  again  the  unsymmetrical  isostere  (N2O)  has  slightly  the 
greater  volume,  as  found  in  comparing  carbon  monoxide  and  nitrogen. 
The  lack  of  symmetry  in  both  cases  is  in  the  distribution  of  positive 
charge  among  the  nuclei  of  the  atoms. 

Elementary  fluorine  is  isosteric  with  the  nuclear  carbon  atoms  of  ethane. 
As,  however,  the  critical  constants  of  the  former  have  not  been  determined, 
no  comparison  can  be  made.  It  will  be  of  interest  to  obtain  a  value  for 
two  tetrahedral  neon  octets  sharing  one  pair,  as  in  ethane.  This  can  be 
done  by  subtracting  6  X  28  for  6  hydrogens  from  the  value  for  ethane 
(286);  thus  286  —  168  =  118  for  the  nuclear  C— C  atoms. 

Summary. — From  the  above  it  results  that  with  one  value  (28)  for 
hydrogen,  80  for  the  cubic  neon  structure,  144  for  2  tetrahedral  neon 
structures  sharing  2  pairs  and  174  when  sharing  3  pairs,  the  volumes  of 
methane,  ammonia,  water,  ethylene,  acetylene,  carbon  monoxide,  oxygen 
and  nitrogen  can  be  reproduced  as  follows. 


Observed. 

Calculated. 

A. 

Van  Laar  calc. 

A. 

CH4 

191 

192 

fl 

156 

—35 

NH3 

165 

164 

—1 

162 

—3 

H20 

136 

136 

0 

138 

+2 

02 

144 

(144)' 

140 

—4 

C2H4 

255 

256 

-hi 

256 

—  1 

N2 

174 

(174)" 

.  .  . 

170 

—4 

C2H2 

229 

230 

-hi 

228 

—  1 

CO 

178 

174 

—4 

170 

—8 

a  Assumed  in  the  calculation. 

The  calculated  values  agree  with  the  observed  within  0.5%  with  the 
exception  of  that  for  carbon  monoxide,  which  is  about  2%  too  low. 

The  results  obtained  in  the  foregoing  analysis  are  taken  to  be  good 
evidence  of  the  correctness  of  the  assumption  that  isosteres,  whether 


8 

existing  alone  as  molecules  or  forming  the  nuclear  atoms  of  hydrides 
have  the  same  volume,  independent  of  the  particular  atoms  involved. 
It  is  very  unlikely  that  all  the  relations  cited  above — namely,  that  the 
volumes  of  methane,  ammonia  and  water  can  be  expressed  with  one 
value  for  all  the  nuclear  atoms  and  another  for  hydrogen,  or  that  this  same 
value  for  hydrogen  and  the  values  for  elementary  oxygen  and  nitrogen  can 
express  the  volumes  of  ethylene  and  acetylene,  respectively — are  simply 
fortuitous.  It  is  true  that  Van  Laar,  making  different  assumptions,  finds 
nearly  as  good  agreement,  with  the  exception  of  his  value  for  methane, 
which  is  seriously  in  error  (156  calculated;  191  observed).  In  order  to 
get  this  agreement,  however,  he  requires  two  values  for  hydrogen,  two 
for  nitrogen  and  one  each  for  carbon  and  oxygen.  In  the  present  analysis, 
one  value  is  used  for  hydrogen  and  three  different  values  are  assigned  to 
the  three  different  arrangements  of  electrons  about  the  nuclear  atoms  met 
with  in  these  compounds. 

Effect  of  Multiple  Bonds. — For  ethane,  ethylene  and  acetylene, 
Van  Laar  uses  a  single  value  each  for  carbon  and  hydrogen,  in  effect 
assuming  that  the  differences  in  volume  among  these  compounds  depend 
wholly  upon  the  number  of  hydrogen  atoms  in  the  different  molecules. 
The  results  recorded  in  this  paper  indicate  that  there  is,  in  addition,  a 
difference  due  to  the  manner  in  which  the  carbon  atoms  are  combined, 
that  is  to  say,  a  difference  due  to  the  type  of  electron  structure.  Ex- 
pressed in  terms  of  the  volume  of  a  single  atom,  the  values  for  a  single 
neon  octet  combined  in  the  various  ways  are:  sharing  no  pairs  (CH4,  etc.) 
80;  sharing  one  pair  (C2H6)  59  (118/2);  sharing  two  pairs  (O2  and  C2H4) 
72  (144/2);  sharing  three  pairs  (N2  and  C2H2)  87  (174/2). 

When  one  pair  is  shared,  the  volume  is  one-quarter  less  (59/80  = 
74%)  than  when  no  pairs  are  shared.  The  similarity  between  the  volumes 
of  the  nuclear  atoms  in  methane,  etc.  (when  no  pairs  are  shared  with 
other  octets)  and  that  of  neon  was  taken  to  indicate  that  the  nuclear 
atoms  in  the  former  are  nearly  cubic.  In  ethane,  the  nuclear  atoms  are 
almost  certainly  tetrahedral.  The  ratio  of  the  volumes  probably  rep- 
resents, therefore,  the  relation  between  the  volumes  of  the  cubic  octet 
and  the  tetrahedral  octet  of  neon. 

When  2  pairs  are  shared,  the  volume  of  a  single  atom  is  13  units 
greater  than  when  one  pair  is  shared  and  when  3  pairs  are  shared, 
there  is  a  further  increase  of  15  units  per  atom.  The  distances 
between  the  centers  of  two  tetrahedra  meeting  (a)  at  their  apexes 
(b)  along  an  edge  (c)  at  a  face,  are  in  the  ratio,  4:3:2.  These 
configurations  correspond  to  the  sharing  of  one,  two  and  three 
pairs,  respectively.  Thus,  the  tendency,  if  unresisted,  on  sharing  2 
and  3  pairs  would  be  to  bring  the  positive  nuclei  at  the  centers  of  the 
tetrahedral  electron  shells  nearer  and  nearer  together.  The  volume  in- 


creases  on  sharing  successively  the  second  and  third  pairs  probably  rep- 
resent the  reaction  of  the  positive  nuclei  against  this  tendency.  By 
attempting  to  get  as  far  apart  as  possible  they  distend  the  molecule. 
This  state  of  tension  due  to  the  multiple  bond  is  evidently  an  element 
of  weakness  and  the  multiple  bond  might  be  expected  to  be  a  seat  of 
chemical  activity,  as  is  known  to  be  the  case. 

Structure  of  Nitrogen. — Langmuir  accounts  for  the  inertness  of 
nitrogen  and  carbon  monoxide  by  assuming  a  condensed  structure  con- 
sisting of  the  2  positive  nuclei  each  holding  a  pair  of  electrons  (corre- 
sponding to  helium)  and  holding  between  them  a  third  pair,  this  structure 
being  surrounded  by  8  electrons  at  the  corners  of  a  cube.  The  alternative 
structure  consists  of  2  octets  sharing  3  pairs,  as  do  the  carbon  atoms  in 
acetylene.  As  the  reactivities  of  nitrogen  and  carbon  monoxide  are  not 
so  great  as  that  of  acetylene,  Langmuir  is  inclined  to  think  the  structures 
cannot  be  similar.  Reactivity  is,  however,  a  rather  vague  term.  It  is 
true  that  nitrogen  is  commonly  spoken  of  as  inert  and  acetylene  as  active 
chemically.  Yet  if  the  strength  of  the  bond  joining  the  nuclear  atoms  be 
measured  by  the  tendency  of  the  two  compounds  to  dissociate,  the  one 
into  nitrogen  atoms  and  the  other  into  CH  radicals,  the  stabilities  must 
certainly  be  assumed  to  be  of  the  same  order. 

As  pointed  out  in  the  first  part  of  this  paper,  there  is  good  evidence  that 
the  volumes  of  elementary  nitrogen  and  the  two  carbon  atoms  of  acetylene 
are  the  same,  thus  indicating  a  similarity  in  structure.  Furthermore, 
one  would  expect  such  a  very  condensed  structure  as  Langmuir  suggests 
for  nitrogen,  the  outermost  electrons  of  which  form  only  a  single  octet, 
to  have  a  decidedly  smaller  volume  than  elementary  oxygen,  for  example, 
the  outer  shell  of  which  consists  of  two  octets  of  electrons  sharing  two 
pairs;  or  of  argon,  which  consists  of  a  single  positive  nucleus  (but  with 
a  positive  charge  of  18),  a  pair  of  electrons  and  two  octets  of  electrons 
one  outside  the  other.  Actually,  the  volumes  of  elementary  oxygen  and 
of  argon  are  both  144,  while  that  of  elementary  nitrogen — 174 — is  de- 
cidedly larger  than  either. 

The  fact  that  the  volume  of  elementary  nitrogen  is  greater  than  that  of 
elementary  oxygen  also  has  a  bearing  on  the  general  assumption  made 
in  this  paper,  that  it  is  principally  the  particular  arrangement  of  electrons 
rather  than  the  charge  on  the  positive  nuclei  which  determines  the  volume 
of  an  atom  or  group  of  atoms.  Since  the  positive  nuclei  of  oxygen  atoms 
possess  a  charge  of  +8  while  that  of  the  nitrogen  atoms  is  +7,  one  might 
have  expected  that  the  greater  repulsion  between  the  larger  nuclei  of 
oxygen  would  have  given  to  elementary  oxygen  the  greater  volume. 
That  it  is  distinctly  less  in  volume  than  is  elementary  nitrogen,  with 
-f-7  positive  nuclei,  indicates  that  the  volume  is  more  influenced  by  other 
factors.  The  other  apparent  difference  between  the  compounds,  accord- 


10 

ing  to  the  theory,  being  in  the  number  and  arrangement  of  the  electrons— 
the  limiting  boundaries  of  the  molecules — it  is  reasonable  to  refer  the 
volume  relation  rather  to  this. 

Nitric  Oxide. — Nitric  oxide  is  peculiar  in  having  an  odd  number  of 
electrons  (15).  It  is  thus  intermediate  between  elementary  nitrogen  with 
14,  and  elementary  oxygen  with  16  electrons.  Langmuir  has  suggested 
that  it  may  have  essentially  the  structure  which  he  assigns  to  elementary 
nitrogen,  the  extra,  odd  electron  being  "imprisoned  in  the  octet  com- 
prising the  shell."  As  this  structure  for  nitrogen  has  been  rendered 
doubtful  by  the  preceding  considerations  it  will  be  of  interest  to  find 
what  other  structure  is  possible  and  what  are  the  indications  furnished 
by  the  volume  of  the  substance. 

The  volume  of  nitric  oxide  is  surprisingly  small,  128.  that  of  oxygen 
being  144  and  nitrogen,  174.  It  is  in  fact  actually  nearer  that  of  the 
carbon  atoms  in  ethane  (118).  Nitric  oxide  contains  one  more  electron 
than  nitrogen  and  it  is  possible  that  in  the  former  the  octets,  like  those  in 
nitrogen,  share  3  pairs,  the  odd  electron  being  at  the  center  of  the  triangle 
formed  by  these  3  pairs,  directly  between  the  2  positive  nuclei  and  held  in 
place  by  the  attraction  of  the  latter.  The  odd  electron  so  placed  would 
certainly  tend  to  draw  the  nuclei  together,  lessening  the  distention  of  the 
molecule  and  making  the  volume  of  the  molecule  less  than  that  of  ele- 
mentary nitrogen.  Actually  the  volume  is  reduced  nearly  to  the  normal 
volume  of  2  octets  sharing  a  single  pair  as  exemplified  by  the  carbon 
atoms  in  ethane.  In  the  latter  case  the  shared  electron  pair  is  also  placed 
directly  between  the  2  positive  nuclei. 

The  odd  electron  placed  as  suggested  above  would  certainly  be  held 
under  rigid  constraints.  Lewis,1  who  would  attribute  color  in  com- 
pounds to  weakly  held  electrons,  has  pointed  out  that  of  the  substances 
containing  an  odd  number  of  electrons,  only  nitric  oxide  is  colorless, 
that  is  to  say,  all  the  electrons  including  the  odd  are  rigidly  held. 

Hydrocarbons,  Amines  and  Ethers. — There  are  a  few  hydrocarbons, 
amines  and  ethers  for  which  data  are  available  whose  chains  of  nuclear 
atoms  are  isosteric  and  should,  therefore,  have  equal  volumes.  A  com- 
parison of  the  5-  and  3-atom  chains  is  given  below.  The  volumes  of  the 
chains  have  been  obtained  by  subtracting  28  for  each  hydrogen  atom  from 
the  volumes  of  the  compounds.  It  should  be  borne  in  mind  that  this 
method  throws  all  the  experimental  error  on  the  volume  of  the  chain. 
5-Atom  chains.  3-Atom  chains. 

b  X  106.  28  H.  Chain.  b  X  10.  28  H.  Chain. 

*  w-C6Hi2  652  —  336  =  316  C3H8  385  —  224  =  161 

(C2H6)2NH         621  —  308  =  313  C2H6NH2  376  — 196  =  180 

(C2H5)2O  600  —  280  =  320  (CH3)2NH          382  — 196  =  186 

(CH3)2O  346  —  168  =  178 

1  Loc.  cit. 


11 

With  the  exception  of  the  value  obtained  from  propane,  the  agreement 
is  satisfactory  within  each  series. 

Hydrocarbon  Chains.  —  As  is  well  known,  the  volumes  of  compounds 
containing  long  chains  of  carbon  atoms  are  not  strictly  additive.  The 
values  for  the  increment  CH2  usually  rise  in  ascending  a  series.  This 
is  true  of  the  values  of  b  for  the  straight-chain  hydrocarbons,  as  will  be 
seen  from  the  following  comparison  of  observed  values  with  those  calcu- 
lated from  the  values  H  =  28  and  C  =  59  (as  found  in  ethane). 

Observed.         Calc.  % 

C2H6  ...............................  286  (286) 

C3H8  ..................  .............  385  401  16  4.2 

«-C6H12  .......  .  .....................  652  631  21  3.2 

w-C6H14  .............................  785  746  39  5.0 

w-C7Hi6  .............................  919  861  58  6.3 

w-C8Hi8  ......  ..............  .........  1057  976  81  7.7 

(CH3)2CH.CH2CH3  ...................  641  631  10  1.6 

(CH3)2CH.CH(CH3)2  .................  745  746  1  0.1 

(CH3)2CH.CH2CH2CH(CH3)2  ..........  1025  976  49  4.8 

For  the  straight  chain  compounds,  the  percentage  by  which  the  ob- 
served values  exceed  the  calculated  steadily  increases,  with  increasing 
number  of  atoms. 

The  branched  chain  isomers  have  volumes  smaller  than  the  straight 
chain  and  therefore  nearer  the  calculated  values.  It  is  of  interest 
to  note  that  that  compound  in  which  the  relative  amount  of 
departure  from  the  straight  chain  is  greatest,  namely,  di-«0-propyl, 


H.CH       ,  has  a  volume  almost  identical  with  that  calculated  (745 

CH 

observed;  746  calculated). 

Ring  Structures.  —  It  is  of  interest  to  find  what  values  are  obtained 
for  ring  structures.  The  value  for  toluene  will  first  be  examined.  The 
radical,  C6H5,  should  have  a  volume  equal  to  that  of  benzene  less  one 
hydrogen  atom  or  537  —  28  =  509.  The  volume  of  CH3  should  be  59  + 
(3  X  28)  =  143.  The  sum  of  these  gives  the  value  for  toluene,  C6H5CH3, 
652.  The  observed  value  is  653. 

For  the  rings  in  benzene  and  cyclohexane,  the  following  values  are  ob- 
tained by  subtracting  for  the  total  number  of  hydrogen  atoms  :  C6H6,  537  — 
(6  X  28)  =  369;  C6H12,  635  —  (12  X  28)  =  299. 

The  unsaturated  benzene  ring  has  the  greater  volume.  This  is  in 
agreement  with  the  relations  already  found  between  the  volumes  of 
saturated  and  unsaturated  nuclear  atoms.  The  carbon  atoms  in  cyclo- 
hexane might  have  been  expected  to  have  the  volume  59  each.  Actually 
the  volume  is  299/6  =  50.  The  ring  structure  appears  to  be  very  much 
condensed. 


12 

Phosphine  and  Hydrogen  Sulfide.— Data  are  not  available  for  enough 
compounds  having  nuclear  atoms  related  to  argon,  as  those  just  discussed 
are  related  to  neon,  to  allow  very  satisfactory  comparisons  to  be  made. 
There  are  dependable  values  for  phosphine,  hydrogen  sulfide  and  hy- 
drogen chloride,  however,  and  these  will  be  analyzed  so  far  as  possible. 

If,  as  in  the  case  of  methane,  ammonia  and  water,  the  difference  be- 
tween the  volumes  of  phosphine  and  hydrogen  sulfide  (230  —  192  =  38) 
be  taken  as  the  volume  of  one  hydrogen  in  these  substances,  then  for  the 
volumes  of  the  nuclear  atoms,  one  obtains:   PH3,  230  —  (3  X  38)  =  116; 
H2S,  192  —  (2  X  38)  =  116.     Because     of     the     method     of     treatment 
the    value    for    the    nuclear    atom    is   necessarily   the   same    in    both 
cases.     This   value    (116)    is    116/144   or   80%    of    that    of    the    cor- 
responding  rare   gas,    argon.     A   carbon   atom   hi   ethane   sharing   me 
pair    (and   in   the    tetrahedral    form)    has    a    volume    59/76,    or    78% 
of   that   of   the   corresponding   cubical   atom,    neon.     As   the   volumes 
of  the  nuclear  atoms  in  phosphine  and  hydrogen  sulfide  bear  nearly  the 
same  numerical  relation  to  that  of  the  corresponding  cubic  atom,  argon, 
it  would  appear  that  already  in  the  simple  hydrides  the  nuclear  atoms 
related  to  argon  are  tetrahedral.     The  hydrogen  atoms  by  their  attrac- 
tion for  pairs  of  electrons  appear  to  have  been  able  to  deform  the  argon 
(cubic)   structure  to  such  an  extent  that  it  is  essentially  tetrahedral. 
As  the  volume  of  argon  is  nearly  twice  that  of  neon  (144,  76)  one  might 
have  expected  this  relatively  greater  deformation  of  the  former  structure. 
Volume  of  Hydrogen. — The  volume  of  hydrogen  in  these  compounds 
appears  to  be  greater  than  in  those  compounds  containing  nuclear  atoms 
related  to  neon.     This  is  undoubtedly  the  effect  of  the  very  much  larger 
charge  on  the  positive  nuclei  of  atoms  related  to  argon.     The  hydrogen 
atom  in  each  of  these  compounds  actually  consists  only  of  a  singly  charged 
positive  nucleus  of  exceedingly  small  volume  held  by  means  of  an  electron 
pair  of  the  nuclear  atom  but  repelled  by  its  positive  nucleus.     Its  con- 
tribution to  the  volume  therefore,  depends  on  the  equilibrium  position 
it  holds  with  respect  to  the  electron  pair  and  positive  nucleus  of  the 
nuclear  atom.     If  it  is  forced  out,  its  apparent  volume  will  be  greater 
and  vice  versa..    The  hydrogen  atom  cannot  be  expected,  therefore,  to 
have  a  constant  volume.     This  is  emphasized  by  the  fact  that  in  the 
elementary  state   (b  —  11.9  X  10~8),  the  atom  has  the  relatively  very 
great  volume  of  60.     The  greater  apparent  volume  of  hydrogen  in  hy- 
drogen sulfide  as  contrasted  with  that  in  water  is  indicative  of  the  greater 
ease  of  ionization  of  the  former  compound — the  hydrogen  nucleus  is 
normally  separated  from  the  nuclear  atom  to  a  greater  extent.     It  may 
be  pointed  out  here  that  Van  Laar's  values  of  14  for  hydrogen  combined 
with  carbon  and  34  for  hydrogen  combined  with  any  other  atom,  are  not 
so  easily  explained.     Although  carbon  is  a  very  peculiar  element,  it  is 


13 

not  so  markedly  different  from  all  other  elements,  on  the  basis  of  the 
theory,  as  to  lead  one  to  expect  any  such  distinction  between  the  volume 
of  hydrogen  associated  with  it  and  associated  with  any  other  element. 
One  would  rather  expect  either  a  different  value  for  hydrogen  combined 
with  each  element  or  compound,  increasing  with  increasing  atomic 
weight  of  the  element  or  else  for  each  rare  gas  type  of  nuclear  atom,  as 
apparently  is  the  case.1 

Hydrogen  Chloride. — The  treatment  of  the  value  for  hydrogen 
chloride  presents  certain  difficulties.  One  is  prepared  to  find  a  structure 
rather  different  from  any  of  those  so  far  considet-ed  because  of  the  strongly 
polar  nature  of  the  compound.  The  value  (182)  is  clearly  relatively 
greater  than  that  of  hydrogen  sulfide,  since  with  one  less  hydrogen,  the 
value  is  only  10  less  (192,  182).  If  38,  the  value  for  hydrogen  in  phos- 
phine  and  hydrogen  sulfide  be  subtracted  from  the  hydrogen  chloride 
value,  the  remainder  (182  —  38  =  144)  is  precisely  the  value  of  argon 
itself.  The  chlorine  atom  in  hydrogen  chloride  thus  appears  to  have  the 
cubic  structure,  one  hydrogen  being  insufficient  to  force  the  atom  into  the 
tetrahedral  form.  This  is,  of  course,  just  the  form  (i.  e.,  cubic)  which  the 
halogen  and  alkali  atoms  are  supposed  to  have  in  alkali  halide  crystals, 
the  alkali  halides  being  also  highly  polar.  The  assumption  of  the  cubic 
argon  structure  by  the  chlorine  atom  in  hydrogen  chloride  may  serve  in 
some  degree  to  account  for  the  difference  in  properties  between  hydrogen 
chloride  and  hydrogen  sulfide. 

Chlorine. — The  various  determinations  of  the  critical  constants  for 
elementary  chlorine  are,  unfortunately,  widely  divergent.  The  values  for 
b  X  10+5  are  226  (Dewar)  205  (Knietsch,  1890)  and  252  (Pellaton,  1915), 
giving  the  values  113,  103  and  126  for  one  chlorine  atom.  Van  Laar 
chooses  to  take  Dewar's  value  (113),  which  is  not  far  from  that  found 
here  for  the  nuclear  atoms  in  phosphine  and  hydrogen  sulfide  (116). 
The  latter  were  assumed  to  be  more  nearly  tetrahedral.  Two  octets 
sharing  one  pair  with  no  combined  hydrogen  atoms  may  not  be  tetra- 
hedral, however.  Undoubtedly  the  attraction  of  the  2  positive  nuclei 
will  tend  to  draw  the  shared  electrons  toward  the  line  joining  the  nuclei, 
thus  deforming  the  cubic  structure,  and  the  volume  of  the  molecule  will 
at  least  be  less  than  that  of  2  cubic  structures  with  volume  144  (argon) 
each.  Pellaton's  recent  value  of  126  for  each  atom  in  elementary  chlorine 
seems  best  to  fulfil  the  requirements,  since  it  is  midway  between  that  of  the 
1  It  is  possible  that  the  apparent  volume  of  the  hydrogen  atom  does  increase  slightly 
as  the  charge  on  the  positive  nucleus  of  the  nuclear  atom  increases  but  that  this  is  offset 
by  the  fact  that  the  electron  shell  about  the  nuclear  atom  decreases  slightly  in  volume 
with  increasing  nuclear  change — the  electrons  are  displaced  inward  somewhat.  It  is, 
in  fact,  possible  to  get  slightly  better  agreement  assuming  a  slight  regular  increase  in 
volume  for  hydrogen  and  decrease  in  volume  for  the  nuclear  atom  with  increase  in  charge 
on  the  positive  nucleus  of  the  nuclear  atom,  in  any  given  series 


14 

tetrahedral  atoms  in  phosphine  and  hydrogen  sulfide  (116)  and  that  of  the 
cubic  atom,  argon  (144),  corresponding  to  a  deformed  cube  structure. 

Atoms  Similar  to  Krypton  and  Xenon. — It  is  not  possible  to  make  an 
analysis  of  the  volumes  of  compounds  containing  nuclear  atoms  related 
to  krypton  and  xenon  because  critical  data  have  only  been  determined 
for  one  or  two.  Since,  according  to  Langmuir,  the  outer  shell  of  these 
atoms  is  made  up  of  18  instead  of  8  electrons,  one  cannot  apply  the  results 
already  arrived  at  to  the  examination  of  these  few  compounds.  There 
are,  however,  two  series  of  compounds  the  volumes  of  which  yield  in- 
teresting results.  These  are  the  tetrachlorides  of  carbon,  germanium 
and  tin  and  fluoro-,  chloro-,  bromo-  and  iodobenzene. 

The  Tetrachlorides  of  Carbon,  Germanium  and  Tin. — If  the  carbon 
atom  in  carbon  tetrachloride  (566)  be  taken  to  be  tetrahedral  (59),  as  it 
almost  certainly  is,  since  it  shares  all  four  pairs,  there  is  obtained  for  the 
volume  of  one  chlorine  ((566  —  59/4)  =  127).  This  is  very  close  to 
Pellaton's  recent  value  for  one  chlorine  atom  in  elementary  chlorine 
(126).  If  127  be  taken  as  the  volume  of  one  chlorine  in  ger- 
manium and  tin  tetrachlorides,  one  obtains  for  the  volume  of  ger-. 
manium  and  tin  GeCl4,  663— 507  =  156  =  Ge;  SnCl4,  733— 507  =  226  =  Sn. 
The  volumes  of  the  corresponding  rare  gases  are  krypton  177,  and  xenon, 
228.  The  value  for  tin  (226)  is  close  to  that  of  the  corresponding  rare 
gas,  xenon  (228),  indicating  that  the  shell  of  18  electrons  has  not  been 
greatly  deformed.  As  the  electrons  are  probably  closer  together  than  in 
the  shell  of  chlorine,  it  is  not  impossible  that  the  chlorine  might  be  de- 
formed cubic  and  the  tin  atom  still  have  essentially  the  structure  of  the 
rare  gas,  xenon.  The  value  for  germanium  (156)  is  somewhat  less  than 
that  of  the  rare  gas,  krypton  (177),  to  which  it  corresponds.  This  would 
seem  to  indicate  some  deformation.  However,  of  the  two,  greater  weight 
must  be  attached  to  the  value  for  tin,  since  the  constants  for  tin  tetra- 
chloride are  those  of  Young  while  the  constants  of  germanium  tetra- 
chloride were  determined  by  Nilson  and  Petterson  (1887)  and  represent, 
so  far  as  known,  the  only  determinations  of  critical  constants  published 
by  these  authors. 

A  new  determination  of  the  critical  constants  of  germanium  tetra- 
chloride and  a  determination  of  those  of  silicon  tetrachloride  would  be  of 
great  value  in  this  connection. 

The  Aromatic  Halogen  Compounds. — The  value  for  benzene  is  537. 
Subtracting  28  for  one  hydrogen,  the  value  537 — 28  =  509  is  obtained 
for  the  phenyl  radical,  CeH5.  If  this  value  be  subtracted  from  those  of  the 
aromatic  halogen  compounds,  the  remainder  should  be  the  volume  of  the 
halogens :  C6H5F,  574—509  =  65  =  F ;  C6H5C1,  648—509  =  139  =  Cl ;  C6H6Br, 
687— 509  =  178  =  Br;  C6H6I,  740—509  =  231  =  1. 

For  fluorine,  a  value  between  59  (tetrahedral)  and  80  (cubic)  was  to 


15 

have  been  expected.  The  value  found  is  65.  For  chlorine,  the  value 
126  was  looked  for.  Actually  a  value  (139)  somewhat  nearer  that  of 
argon  (144)  was  obtained.  For  bromine  (178)  and  iodine  (231),  values 
close  to  those  of  the  corresponding  rare  gases,  krypton  (177)  and  xenon 
(228)  are  obtained,  as  in  the  case  of  tin  in  tin  tetrachloride.  As  bromine 
and  iodine  each  share  with  the  radical  only  one  pair  out  of  18  electrons, 
one  would  certainly  not  expect  any  great  deformation,  and  little  apparently 
occurs. 

Volumes  of  the  Rare  Gasses. — According  to  Langmuir,1  "the  electrons 
in  any  given  atom  are  distributed  through  a  series  of  concentric  shells, 
all  of  equal  thickness.  Thus,  the  mean  radii  of  the  shells  form  an  arith- 
metic series,  1,  2,  3,  4 "  These  shells  contain  2  sets  of  electrons. 

Thus  in  xenon,  the  first  shell  contains  the  2  electrons  corresponding  to 
helium,  the  second  shell  contains  the  2  octets  of  electrons  corresponding 
to  the  outermost  electrons  of  neon  and  argon,  respectively,  and  the  third 
shell  contains  the  2  sets  of  18  electrons,  one  outside  the  other,  corre- 
sponding to  the  outermost  electrons  of  krypton  and,  finally,  xenon  itself. 
It  is  specifically  stated  that  this  relation  of  the  radii  of  the  shells  holds 
only  for  one  given  atom.  It  will,  however,  be  of  interest  to  see  if  any 
uch  simple  relation  holds  for  different  atoms. 

If  the  radii  are  in  the  ratio  1  :  2  :  3,  the  mean  volumes  of  the  shells 
must  be  as  1  :  8  .:  27.  If  the  mean  volume  of  a  given  shell  is  the  same  in 
every  atom  which  contains  it,  then  it  might  be  expected  that  the  mean  of 
the  volumes  of  neon  and  argon,  representing  the  second  shell  (helium 
accounts  for  the  first)  and  of  krypton  and  xenon,  representing  the  third 
shell,  would  be  to  each  other  as  8  :  27.  The  values  actually  obtained  are 
(76  +  144) /2  =  110;  and  (177  +  228)/2  =  202.5.  The  mean  of  the 
volumes  of  neon  and  argon  is  110,  that  of  krypton  and  xenon,  202.5. 
These  are  clearly  not  in  the  ratio  required.  In  krypton  and  xenon,  it  is 
quite  possible  that  because  of  the  larger  charge  on  the  positive  nucleus, 
the  electrons  of  the  second  shell  will  be  drawn  inward  more  than  the 
corresponding  electrons  in  neon  and  argon  and  the  mean  volume  of  the 
shell  be  enough  smaller  than  in  neon  and  argon  to  satisfy  the  relation.2 

1  THIS  JOURNAL,  41,  932  (1919). 

2  It  is  of  interest  to  note  that  the  volumes  of  the  rare  gases  are  roughly  proportional 
to  the  square  roots  of  their  atomic  weights  as  will  be  seen  from  the  following  table. 

b. 

b.  At.  wt.  VAt.  wt.  VAt.  wt. 

Ne 76  20  4.47  17.0 

A 144  40  6.32  22.8 

Kr 177  83  9.11  19.4 

Xe.... 228  130  11.4  20.0 

In  fact,  rough  average  agreement  can  be  obtained  for  molecular  volumes  (in  general) 

if  they  are  assumed  to  be  proportional  to  the  sum  of  the  square  roots  of  the  atomic 

weights  of  the  constituent  atoms. 


16 

Two  facts,  in  particular,  are  brought  out  by  the  foregoing  analysis. 
First,  isosteric  atoms,  molecules  and  groups  appear  to  have  the  same 
volume  regardless  of  the  particular  kinds  of  atoms  of  which  they  are 
composed.  In  other  words,  the  number  and  arrangement  of  electrons 
in  the  outer  shells  of  atoms  or  groups  of  atoms  is  the  predominating  factor 
in  determining  their  volume.  Second,  the  volumes  of  other  atoms, 
particularly  of  the  more  complex  ones,  are  intimately  related  to  the 
volumes  of  the  rare  gases. 

It  is  realized  that  the  possibilities  of  the  method  of  treatment  used 
in  this  paper  are  by  no  means  exhausted  and  the  writer  expects  at  some 
future  time  to  consider  further  the  implications  of  the  present  work. 

Summary. 

1.  An  analysis  of  molecular  volumes,  as  determined  from  the  critical 
data,  has  been  made  from  the  point  of  view  of  the  Lewis-Langmuir  theory 
and  especially  of  Langmuir's  theory  of  isosteres. 

2.  Evidence  has  been  brought  forward  to  show  that  isosteric  molecules 
and  nuclear  atoms  in  hydrogen  compounds  have  the  same  volume.     The 
volume  depends,  therefore,  on  the  number  and  arrangement  of  electrons 
surrounding  the  positive  nuclei  of  the  atoms  rather  than  on  the  charges 
on  the  nuclei,  that  is  to  say,  on  the  particular  kinds  of  atoms  concerned. 
Thus,  it  has  been  shown  that  the  nuclear  carbon,  nitrogen  and  oxygen 
atoms  of  methane,  ammonia  and  water,  respectively,  have  the  same 
volume. 

3.  It  has  been  shown  that  the  carbon  atoms  in  ethane,  ethylene  and 
acetylene   have   volumes   increasing   with   the   degree   of   unsaturation. 
The  same  observation  holds  in  comparing  the  carbon  atoms  in  benzene 
and  cyclohexane.     The  volumes  of  atoms  thus  increase  with  the  number 
of  electron  pairs  shared.     An  explanation  of  this  has  been  presented. 

4.  It  has  been  shown  that  elementary  nitrogen  and  carbon  monoxide 
probably  have  the  normal  or  acetylenic  structure,  3  pairs  being  shared, 
rather  than  the  condensed  structure  suggested  by  Langmuir. 

5.  A  structure  for  nitric  oxide  has  been  suggested  and  evidence  in  its 
favor  produced. 

6.  The  volumes  of  the  rare  gases  have  been  considered  from  the  point 
of  view  of  Langmuir. 

The  writer  is  especially  indebted  to  Professors  H.  S.  Taylor  and  Alan 
W.  C.  Menzies  for  criticism  and  suggestions  regarding  the  work  sum- 
marized in  this  paper. 


INITIAL  FINE  OF  25  CENTS 


YC   10961 


Gay  lord  Bros. 

Makers 
Syracuse,  N.  Y. 

PAT.  JAN.  21,  1908 


453565 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


